From the above, we can see that \(L_R(\mathcal {E})\)  can be regarded as the first order approximation error for
\(\widetilde{\mathcal {P} }_R - \widehat{\mathcal {P} }_R\) , while \(S_R(\mathcal {E})\)  as the higher order error. In fact, according to Lemma 2 of [1]}, the two terms \(L_R(\mathcal {E})\)  and \(S_R(\mathcal {E})\)  can be bounded as below.
